I'm animating a picture, have the limbs on different layers, so I can just simply use the free transform tool to rotate them into the good position. Although it's a pain to always reset the pivot point from the center. Is there a way to make Photoshop remember where I want the pivot point to be?

Doug's method is very good. A couple of variations - you can use a rectangle rather than a circle. The transform bounding box will change size with each rotation, but will always be centered on the pivot point. Whether circle or rectangle, you can combine step 1 and step 2 by dragging a marquee "out from center" from the desired pivot point so that it just encloses the object.

You could also do this without an additional layer, by filling the selection on the same layer as the object with 1% opacity, using the Behind mode. This could cause problems if you wanted to se a different pivot point later, though.

You could even set up several possible pivot points. Select your object and the desired "Pivot Layer", and do your rotation. Then, for each other Pivot Layer, Edit > Transform > Again.